nanoscale topography and spatial light modulator...

Nanoscale topography and spatial lightmodulator characterization using

wide-field quantitative phase imaging

Gannavarpu Rajshekhar,1 Basanta Bhaduri,1 Chris Edwards,2 RenjieZhou,2 Lynford L. Goddard,2 and Gabriel Popescu1,∗

1Quantitative Light Imaging Laboratory, Department of Electrical and ComputerEngineering, Beckman Institute for Advanced Science and Technology, University of Illinois at

Urbana-Champaign, Urbana-61801, Illinois, USA2Photonic Systems Laboratory, Department of Electrical and Computer Engineering, Micro

and Nanotechnology Laboratory, University of Illinois at Urbana-Champaign, Urbana-61801,Illinois, USA

∗[email protected]

Abstract: We demonstrate an optical technique for large field of viewquantitative phase imaging of reflective samples. It relies on a common-pathinterferometric design, which ensures high stability without the need foractive stabilization. The technique provides single-shot, full-field androbust measurement of nanoscale topography of large samples. Further, theinherent stability allows reliable measurement of the temporally varyingphase retardation of the liquid crystal cells, and thus enables real-timecharacterization of spatial light modulators. The technique’s applicationpotential is validated through experimental results.

© 2014 Optical Society of America

OCIS codes: (110.3175) Interferometric imaging; (120.3930) Metrological instrumentation;(070.6120) Spatial light modulators; (120.5050) Phase measurement.

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#201422 - $15.00 USD Received 15 Nov 2013; revised 20 Dec 2013; accepted 14 Jan 2014; published 5 Feb 2014(C) 2014 OSA 10 February 2014 | Vol. 22, No. 3 | DOI:10.1364/OE.22.003432 | OPTICS EXPRESS 3432

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1. Introduction

Nanoscale measurement of surface topography is an important problem for material character-ization and inspection [1]. Some of the prominent topography measurement techniques includethe stylus profilometer [2], atomic force microscope (AFM) [3], scanning electron microscope(SEM) [4], and optical interferometric techniques such as scanning white light interferome-ter [5], phase-shifting interferometer [6], digital holography method [7] and Fizeau interferom-eter [8–10]. However, the stylus, AFM and SEM techniques are invasive, and are hence notsuitable for non-destructive testing and evaluation. Also, the AFM and SEM techniques havelow throughputs, and are not feasible for inspecting large samples. Though the scanning andphase-shifting interferometers are non-invasive, they require multiple scans or phase-shiftedframes, and are hence not suitable for dynamic measurements. Also, the interfering beamsin phase-shifting interferometer and digital holography travel in separate paths, making themmore susceptible to external disturbances and vibrations. Though the Fizeau interferometer hasa common-path geometry, it requires the addition of an additional reference surface which in-fluences the fringe contrast, and is prone to multiple reflections.

In addition to surface topography, the optical interferometric techniques have also been ap-plied for refractive index measurements on account of their high sensitivity to optical pathlength changes; a measurement capability not possible with the stylus, AFM and SEM tech-niques. In particular, a prominent application has been spatial light modulator (SLM) char-acterization by phase retardation measurement [11–13]. The SLM is a wavefront modulationdevice, capable of modulating the polarization, amplitude or phase of the incident light. Whena pattern is projected on the SLM, it causes a change in orientation of the birefringent liquidcrystal molecules depending on the grayscale values of the pattern, and the reflected light isphase-shifted or retarded with respect to the incident light. By changing the grayscale value ofthe projected pattern on the SLM, variable phase retardation can be achieved. This has enabled


Fig. 1. Wide-field QPI setup. FC: Fiber Coupler, CL:Collimator lens, P:Polarizer, BS:BeamSplitter, L1-L4:Lenses with 400 mm focal length, L2-L3:Lenses with 75 mm focal length,FP1:Fourier Plane of lens L1, IP:Image Plane, FP2:Fourier Plane of lens L3, M:Mirror.

the application of SLM in diverse areas such as adaptive optics [14], optical tweezers [15], mi-croscopy [16] etc. In particular, temporal characterization of the SLM, i.e. reliable estimation ofthe temporally varying phase retardation is required for several applications [17,18]. However,it remains a challenging problem due to high temporal stability required for the measurement.

Some of these limitations were addressed by the recently proposed common-path opticaltechnique based on diffraction phase microscopy (DPM) [19–21]. However, the high resolutioninstruments developed so far based on this approach have been restricted to limited field of view(FOV) imaging, and cannot be applied for inspecting large regions of interest. Here, we proposea wide-field quantitative phase imaging (wQPI) technique that enables the assessment of largearea samples with high temporal stability and single-shot full-field measurement capability.

2. Setup

The schematic of the setup is shown in Fig. 1. We use a frequency doubled NdYAG laser, withwavelength λ = 532 nm, as the light source, whose output is coupled to a single mode fiberand subsequently expanded and collimated using a lens (CL). We also place a polarizer (P) inthe optical path to control the polarization and intensity of the illuminating beam. The reflectedwave from the sample is guided via the beam splitter (BS) to a 4 f system comprised of thelenses L1 (focal length f1 = 400 mm) and L2 (focal length f2 = 75 mm), with an aperture (8mm diameter) in the Fourier plane FP1. At intermediate image plane IP, we obtain the imageof the sample with a magnification M1 =− f2/ f1.

A blazed diffraction grating (300 lines per mm) is placed at the plane IP, which generatesmultiple diffraction orders, with the positive first order having the highest intensity (blazedorder). The diffracted waves are passed through another 4 f system formed by lenses L3 ( f3 =75 mm ) and L4 ( f4 = 400 mm). The magnification of this 4 f system is M2 = − f4/ f3. Thelens L3 performs the Fourier transform of the diffracted waves in the second Fourier plane(FP2). In plane FP2, a mask is placed, which consists of a pinhole (10 μm diameter) anda circular hole (6 mm diameter). The prior aperture, located in FP1, low-pass filters the beamsuch that the diffracted orders are spatially separated in FP2, i.e. only light from the zeroth orderpasses through the circular hole. The pinhole filters down the blazed order to a point source,so that it approaches a plane wave after passing through the lens L4 (placed at focal distancefrom the pinhole), and acts as the reference wave in our setup. On the other hand, the zerothorder passes through the circular hole, and acts as the signal wave. These signal and referencewaves interfere at an angle at the camera plane resulting in an off-axis interferogram, whichencodes the phase information corresponding to the topography of the sample. For recordingthe interferogram, we used an Andor Neo Scientific CMOS camera (2560 × 2160 pixels, 16bit, 6.5 × 6.5 μm2 pixel size). The large camera sensor size allows us to inspect up to 16.6 ×


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Fig. 2. (a) Temporal standard deviation σt(x,y) of noise in nm. (b) Histogram of σt . (c)Spatial standard deviation σs(t).

14 mm2 area at the sample plane. Note that low pass-filtering at the two apertures in FP1 andFP2 limits the maximum sample spatial frequency to k0NAmin, with k0 = 2π/λ , and lowers thelateral resolution to 1.22λ/NAmin, where NAmin is the numerical aperture corresponding to thesmaller aperture. As the FP2 circular hole is the limiting aperture in our case, the instrumentprovides a resolution of about 87 μm for NAmin = 0.0075. To preserve transverse resolution,the size of the FP2 hole should be greater than or equal to that of the aperture in FP1. However,aliasing in the interferogram begins to occur when the beam diameter exceeds 8 mm [22]. Thus,we used a slightly smaller value (6 mm) to ensure there is no aliasing.

At the camera plane, denoting the signal wave as Us(x,y) and reference wave as Ur(x,y)=U1,a constant, the recorded intensity can be expressed as,

I(x,y) = |Us(x,y)|2 + |U1|2 +2|Us(x,y)||U1|cos[β0x+φ(x,y)] (1)

which is essentially a cosinusoidal fringe pattern with spatial carrier frequency β0 and phasedistribution φ(x,y). Here, we have β0 = 2π/(|M2|Λ), with Λ being the period of the grating.Note that the sampling frequency is ks = 2π/Δx, with Δx being the pixel size, and the maximumspatial frequency of the interferogram given by Eq.(1), is kmax = β0+k0NAmin. For our system,we have ks = 0.97 radian/μm, β0 = 0.35 radian/μm and k0NAmin = 0.09 radian/μm. Hence,the Nyquist sampling criterion, i.e. ks ≥ 2kmax is satisfied [22]. The phase φ(x,y) is related tothe height distribution h(x,y) of the sample as h(x,y) = (λ/4π)φ(x,y). For quantitative phaseextraction, we apply the Hilbert transform [23] which provides the analytic signal associatedwith the real interferogram, and subsequently use Goldstein’s phase unwrapping method [24].

The proposed setup exhibits several salient features: (1) both the reference and the signalwaves traverse a common-path, which provides a compact system with increased robustnessagainst misalignments and external disturbances, and high stability; (2) the net magnification ofthe system M = M1M2 = 1 i.e. unity, which implies that a large field of view can be analyzed;and (3) the diffraction grating introduces an angle between the reference and signal waves,resulting in an off-axis configuration, which permits phase retrieval from a single interferogram.

To characterize the temporal noise of the system, we used a Thorlabs mirror as the sample,and captured 256 time-lapsed interferograms (FOV 1.6 mm × 1.6 mm) at 10 frames/s. Subse-quently, we recovered the height distribution from each interferogram. To analyze the temporalnoise, the standard deviation with respect to time was computed for each pixel in the image.The resulting temporal standard deviation σt(x,y) and its histogram are shown in Fig. 2(a)and Fig. 2(b). The median value of σt was obtained as 0.9 nm, which represents the temporalsensitivity, and indicates the high stability of the setup due to the common-path configuration.Similarly, we also computed the spatial standard deviation for each image; the resulting σs(t)is shown in Fig. 2(c). The median value of σs was obtained as 8.9 nm, which represents thespatial sensitivity of our system.


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(f)Fig. 3. Recorded interferograms for the (a) surface with features and (c) planar surface. Forregions marked with white boxes in (a) and (c), the fringes are shown in (b) and (d). (e)Estimated height map in nm. (f) Histogram of height.

3. Results

To test the system’s performance, we imaged a 1951 USAF resolution target (R3L3S1P) fromThorlabs. This standard target consists of a glass substrate on which the USAF features are de-posited through chromium evaporation. These features exhibit a 120 nm step height differencewith respect to the substrate. Further, to obtain uniform reflectivity, we coated the entire targetwith a gold/palladium layer of 25 ± 1 nm thickness using a Denton Vacuum sputter coater,while preserving the step height difference of the features. The interference image (FOV 5.9mm × 5.7 mm) for the target is shown in Fig. 3(a). For an arbitrarily selected region (markedwhite) in Fig. 3(a), the fringes are clearly visible, as shown in Fig. 3(b). We also recorded thebackground interference image corresponding to a flat region of the target with no features,which is shown in Fig. 3(c), and the related marked region with visible fringes is shown inFig. 3(d). Subtraction of the background phase from the sample phase removes any aberrationsintroduced by the system. Subsequently, the measured height map after background subtractionis shown in Fig. 3(e). Finally, we show the histogram of the height map in Fig. 3(f), which ex-hibits two dominant peaks, one corresponding to the background and the other correspondingto the features. From the histogram, the step height difference was obtained as 120.5 nm, whichis extremely close to the predicted value. These results clearly show the high accuracy of theproposed technique for surface topography measurements involving large FOV samples.

Next, we demonstrate the utility of our technique for dynamic phase retardation measurementin a liquid crystal SLM. For our analysis, we used a liquid crystal on silicon (LCOS) basedHoloeye Pluto phase-only reflective SLM as the sample. The projected pattern on the SLM ata given time instant is shown in Fig. 4(a). For dynamic behavior, the grayscale (GS) valuesof the central region of this pattern were linearly stepped from 0 (black) to 255 (white), with1 level per time interval of 25 ms, whereas the outer region had a constant zero grayscalevalue. Using the high speed (40 frames/s) Andor Neo camera, we recorded several time-lapsedinterferograms (FOV 3.3 mm × 3.3 mm), each corresponding to a particular pattern on theSLM. For the projected pattern in Fig. 4(a), the corresponding recorded interferogram is shownin Fig. 4(b). The temporally varying phase retardation can be expressed as,

φ(x,y, t) =4πλ

Δn(x,y, t)d (2)


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(h)Fig. 4. (a) Projected pattern on SLM. (b) Recorded interferogram. Measured phase retar-dation in radians at (c) t = 0, GS=0, (d) t = 2.5, GS=100, (e) t = 3.75, GS=150, (f) t = 5,GS=200, and (g) t = 6.25 seconds, GS=250 (see Media 1). (h) Temporally varying meanphase retardation.

where Δn = ne − no is the birefringence, with ne and no being the refractive indices along theextraordinary and ordinary axis, and d is the thickness of the liquid crystal in SLM.

For phase extraction, the dynamic case presents an interesting challenge. The phase cor-responding to the central region keeps increasing with time, whereas it remains constant forthe outer region. As a result, for a given time instant, the phase difference between adjacentpixels corresponding to the central region and the outer region can easily exceed π , which isthe phase aliasing limit [24]. Thus, any spatial phase unwrapping algorithm such as the Gold-stein’s method would provide erroneous results. To circumvent this problem, we performedthe unwrapping operation along the temporal direction [25], which avoids phase aliasing. Thecomputed phase retardation values from the interferograms at different time instants are shownin Figs. 4(c)-4(g). Note that we also recorded a background image corresponding to the zerograyscale projected pattern, and performed background subtraction to ensure that the measuredphase has no contributions arising from the SLM height variations or system aberrations. Thetemporally varying phase retardation is also shown in Media 1. Finally, the mean phase retarda-tion, computed along the temporally varying central region is shown in Fig. 4(h). These resultsclearly demonstrate the suitability of the proposed technique for dynamic measurements. Also,due to the inherent stability of the instrument, we can dynamically measure the phase shiftsvs grayscale values across the entire spatial light modular area. Consequently, this approachprovides a new way of real-time spatial light modulator calibration.

4. Conclusions

We introduced a quantitative phase imaging technique for wide-field metrology. Compared tothe existing methods, it offers the ability to analyze large field of view objects with nanometricaccuracy and exhibits high temporal stability for performing high precision measurements, bothstatic and dynamic. In addition, the technique’s advantages include non-invasive nature, single-shot methodology and full-field measurement capability. It has significant application potentialin non-destructive metrology and characterization of liquid crystal modulators.


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Acknowledgments

This research was supported in part by the National Science Foundation (grant CBET-1040462MRI). Gannavarpu Rajshekhar is supported by the Swiss National Science Foundation fellow-ship. We thank Scott Robinson for assistance with sputter coating.


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